Core-level Spectroscopies with FEFF9 and OCEAN

Transcription

1 Soleil Theory Day Synchrotron SOLEIL, Grand Amphi 6/5/2014 Core-level Spectroscopies with FEFF9 and OCEAN J. J. Rehr 1,4 K. Gilmore, 2,4 J. Kas, 1 J. Vinson, 3 E. Shirley 3 1 University of Washington, Seattle, WA 2 ESRF, Grenoble, France 3 NIST, Gaithersburg, MD, USA 4 European Theoretical Spectroscopy Facility Supported by DOE BES

2 Core-level Spectroscopies with FEFF9 and OCEAN GOAL: ab initio theory Accuracy ~ experiment TALK: I. Introduction II. FEFF9 Real-space Green s Function III. BSE k space - JJR - KG

3 ETSF X-ray Spectroscopy Beamline XAS XES XMCD NRIXS RIXS Full spectrum theoretical tools UV XRAY

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5 The team: Rehr-Group + collaborators Thanks to DOE BES, DOE CMCSN, NSF OCI, and the ETSF

6 Theoretical ingredients beyond DFT Excited State Electronic Structure A. Self-energies & mean free paths B. Screened Core-hole C. Nuclear motion: Debye Waller factors

7 Need for corrections to DFT in XAS Cu Ground-state DFT Many-body Expt

8 FEFF9 reference Ab initio RSGF Theory JJR et al., Comptes Rendus Physique 10, 548 (2009) in Theoretical Spectroscopy L. Reining (Ed) (2009)

9 Quasi-particle Theory of XAS Fermi Golden Rule for XAS μ(ω) Quasi-particle final states ψ f Final state rule V coul = V coul + V core hole Non-hermitian self-energy Σ(E) (replaces Vxc)

10 Real-space Green s Function Approach Golden rule via Wave Functions Ψ Paradigm shift: Golden rule via Green s Functions G = 1/( E h Σ ) No sums over final states!

11 Implementation: Real-space FEFF code Core-hole SCF potentials Essential! Applicable to XAS, EELS, XES, XMCD, DAFS, BN 89 atom cluster

12 Application: XANES Pt L 23 Pt L 3 -edge 1.4 Pt L 2 -edge (S. Bare, UOP) Normalized Absorption FEFF calculation Experiment' Normalized Absorption FEFF calculation Experiment PtL3_xmu '98feb002_xmu' PtL2_xmu '98feb004_xm PtL3edge Photon Energy, ev PtL2edge Photon Energy, ev Dirac relativistic FEFF8 code reproduces all spectral features including absence of white line at L 2 -edge

13 Green s Functions & Parallel Calculations Energy E is a parameter! 1/N CPU Natural parallelization Each CPU does one energy

14 Application: RIXS J. Kas et al. Phys. Rev. B 83, (2011) d 2 ¾ d d! =! /! P F Z P M hf j y 2 jmihmj 1jª 0 i E M E 0 +i M 2 ±(! + E 0 E F ): (1) d! 1 ¹ e (! 1 )¹(!! 1 + E b ) j!! 1 i b j 2 ~ XES * XAS

15 Application LDA+ U / GW in FEFF9* O K-edge MnO Add U as correction to GW self energy: V U (r; E) = V SCF (r) + GW (E) + U lm¾ (E) *Phys Rev B 85, (2012)

16 Inelastic losses in XAS & XPS G ++ (ω)= A(ω) = -(1/π) Im g ++ (ω) Extrinsic + Intrinsic - 2 x Interference Many-body XAS Convolution of QP XAS with effective spectral function A(ω) *L. Campbell, L. Hedin, J. J. Rehr, and W. Bardyszewski, Phys. Rev. B 65, (2002)

17 Beyond GW: Cumulant Methods Europhys J. J. B 85, 324 (2012) see also M. Guzzo et al., PRL 107, (2011) arxiv: GW Kernel Extension XPS

18 Application: Charge Transfer Satellites

19 Part II GW-BSE OCEAN

20 Core-Level X-ray Spectroscopy part II Bethe-Salpeter equation Keith Gilmore 1, J J Rehr 2, J Kas 2, J Vinson 3, E Shirley 3 1 ESRF, Grenoble, France 2 University of Washington, Seattle, WA, USA 3 NIST, Gaithersburg, MD, USA

21 Computational Objective Predictive First-principles Minimal free parameters Accurate Versatile Multiple x-ray techniques Variety of physical / chemical systems Efficient s atoms Modest run-times / resources Usable Simple / intuitive interface & inputs Expertise in DFT not required

22 Atomic Multiplets H mult = H h + H e + H eh H h = ε α + ζl S H e = T + U + V H eh = V α r + g ij

23 Bethe-Salpeter Equation conduction band μ ω = 1 π Im 0 d+ e, h H BSE = H e H h + H eh e, h 1 ω H BSE + iη e, h e, h d 0 valence band H e = dr ρ r r r + V xc ρ r + Σ from DFT or DFT+GW H h = E h + χ j iγ j from atomic DFT or HF lifetime Spin-orbit interaction H eh = V X V D V X = drdr ψ 1 r ψ 2 r core level 1 r r ψ 1 r ψ 2 r V D ω = drdr ψ 1 r ψ 2 r ε 1 r, r ; ω r r ψ 1 r ψ 2 r

24 OCEAN: Obtaining Core-Excitations from Ab-initio electronic structure and the NIST BSE solver Primary Developers Eric Shirley NIST John Vinson NIST Group of John Rehr U. Washington Systematically improvable many-body approach to calculating spectra Based on DFT ground-state electronic structure Spectra obtained from 2-particle solutions of the Bethe-Salpeter eq. Several efficiencies make calculations practical XAS, XES, RIXS, NRIXS, Auger, optical absorption

25 OCEAN process flow Input card single file + pseudopotentials useful defaults atomic positions DFT parameters spectrum type (XAS, XES, XRS) edge information (atom, K/L, etc)

26 OCEAN process flow Input card ABINIT GS DFT Quantum Espresso Freely available Well documented, easy to use High functionality, actively developed Plane-wave basis

27 OCEAN process flow Input card ABINIT GS DFT Quantum Espresso Full periodic table of pseudopotenials available NC : yes US : testing PAW : coming soon

28 OCEAN process flow Input card GS DFT Self-energy

29 Self energy corrections GW: often accurate, but slow Many-pole self energy (MPSE) Example: Ice-Ih Fast post-processing; extension of plasmonpole model Calculate loss function (FEFF, optical code) Approximate loss function with a series of poles Use simple electron gas Green s function Im ε q, ω 1 = π g i ω i 2 δ ω 2 ω i (q) 2 Σ k, E i i d 3 q dω V q 2π 3 2π ε q, ω G heg(e, ω, k) Real Imag. JJ Kas et al, Phys Rev B 76, (2007)

30 OCEAN process flow Input card GS DFT Atomic core Self-energy Core hole wavefunction, energy Core electron screening of core hole PAW reconstruction of atomic unoccupied states Transition matrix elements

31 OCEAN process flow Input card GS DFT Atomic core Self-energy Screening

32 Partition space for efficient calculation of screening response W 0 r = ΔV c r + W c sr (r) +W c lr (r) Short-range: detailed RPA screening χ 0 r, r, ω = dω G 0 r, r, ω G 0 r, r, ω + ω Local region: detailed RPA screening Long-range: model dielectric response χ M r, r Random phase approximate = n r + n(r ) d 3 q (2π) 3 eiq (r r ) ε LL 1 (q, n 0 ; ε ) 1 Local region: 2n 0 detailed RPA screening 4π Levine-Louie model dielectric function EL Shirley, Ultramicroscopy 106, 986 (2006)

33 OCEAN process flow Input card GS DFT Atomic core Self-energy Screening BSE XAS XES NRIXS RIXS (opt abs) Spectrum!

34 XAS: K-edges LiF; F K-edge Exp. OCEAN accurately reproduces full range of spectrum FEFF misses excitonic feature, reproduces extended region J Vinson et al, Phys Rev B 83, (2011)

35 XAS: simple L-edges SrTiO 3 Ti L-edge

36 XAS: transition metal L-edges L 3 / L 2 branching ratios Ocean Exp Atom Z Exp OCEAN Ca Fe Co Ni V Fe Co Ni Cu J Vinson and JJ Rehr, Phys Rev B 86, (2012)

37 XAS: molecules / liquids Photon Energy (ev) Experimental reference spectrum from Adam Hitchcock, McMaster University, Ontario, CA unicorn.mcmaster.ca/corex/name-list.html

38 XES: liquid water (with excited-state dynamics) Water O XES unpublished Tokushima et al., Chem Phys Lett (2008)

39 High pressure silicon Phase change at high pressure Diffraction performed on ESRF ID09 Redistribution of electron density from s-p hybridized bonding orbitals to d-character orbitals with strong interstitial weight JS Tse et al, J Phys Chem C (2014)

40 Pressure NRIXS: L-edges measurement calculation Silicon NRIXS Increasing pressure Phase changes Decreasing excitonic peak Increasing metallicity XRS measured on ESRF ID16 JS Tse et al, J Phys Chem C (2014)

41 Optical absorption LiF MgO calculation experiment LX Benedict et al, Phys Rev Lett 80, 4514 (1998)

42 OCEAN: Obtaining Core-Excitations from Ab-initio electronic structure and the NIST BSE solver Predictive First-principles, minimal free parameters Accurate Versatile XAS, XES, (N)RIXS, optical spectra Periodic crystals, liquids, molecules Efficient 100s atoms (want 1000s) Needs cluster, but not supercomputer Development of release version in progress locally available at the ESRF/Grenoble

43 See poster for additional results Semiconductor nanocrystals Organic electronics Vibrational effects Water CP Schwartz et al, J Chem Phys 130, (2009)

44 Explicit inclusion of vibronic coupling: SrTiO 3 3d 0 ground state e Born-Oppenheimer surfaces 3d 1 excited state e Q q Q e undistorted cubic lattice Q q Q e Important local vibrational modes Q q Ti 4+ O 2- Q e

45 Explicit inclusion of vibronic coupling: SrTiO 3 ԑ (n q,n e ) (0,0) (1,0) (0,1) (1,1) (0,0) H W W 0 (1,0) W H 0 W (0,1) W 0 H W (1,1) 0 W W H 60 (N,N) (N,N) 60 N=200 vibrational levels required for convergence H = H mult + ħw(n q +n e ) 1 mult K Gilmore and EL Shirley, J Phys : Condens Matter 22, (2010)